Comparative NMR Properties of H2 and HD in Toluene-d8 and in H2/HD@C60†

Judy Y.-C. Chen,‡ Angel A. Martı,‡,⊥ Nicholas J. Turro,‡,* Koichi Komatsu,§ Yasujiro Murata,§

and Ronald G. Lawler|

Department of Chemistry, Columbia UniVersity, New York, New York 10027, Institute for Chemical Research,Kyoto UniVersity, Kyoto 611-0011, Japan, and Department of Chemistry, Brown UniVersity,ProVidence, Rhode Island 02912

ReceiVed: March 30, 2010; ReVised Manuscript ReceiVed: April 27, 2010

Spin-lattice relaxation times, T1, have been measured from 200-340 K for the protons in H2 and HD moleculesdissolved in toluene-d8 and incarcerated in C60. It is found that HD relaxes more slowly than H2 in bothenvironments and at all temperatures, as expected from the smaller values of the spin-rotation and dipole-dipolecoupling in HD compared to H2. More detailed analysis using models developed to describe relaxation inboth condensed media and the gas phase indicates that transitions among the rotational states of H2 occur ata rate similar to those of HD in both toluene-d8 solution and in C60, in contrast to the situation in gas phasecollisions between hydrogen and He or Ar, where the lifetimes of rotational states of HD are markedly shorterthan those for H2. Measurements of the relative 1H chemical shifts of H2 and HD, the coupling constant JHD,and the widths of the HD peaks at various temperatures revealed only small effects with insufficient accuracyto warrant more detailed interpretation.

Introduction

In a previous communication1 we compared the protonspin-lattice relaxation time, T1, for H2 in several organicsolvents with that in H2@C60 dissolved in the same solvents.The results were analyzed assuming the relaxation to be dueprimarily to the spin-rotation and dipole-dipole interactionsat high and low temperatures, respectively. Using this asymptoticmodel, it was concluded that, at both high and low temperaturesH2 in toluene-d8 reorients itself ca. 10 times faster than inH2@C60 dissolved in the same solvent. We were, however,unable to achieve a quantitative fit to the T1 data over the fulltemperature range of 200-330 K using either the Hubbardtheory2 for relaxation in liquids or the Schwinger-Bloembergentheory3 of relaxation in slowly equilibrating rotational states ofH2, which has been used with modifications4 to describerelaxation in the gas phase. An empirical fit of the temperaturedependence of a similar set of measurements of T1 for H2 invarious organic solvents5 required four parameters, includingtwo activation energies. Earlier measurements of T1 for H2 inD2O6 yielded an estimate of the reorientation correlation timeat each of several temperatures but employed the assumptionof a fixed ratio of the correlation times for dipole-dipole andspin-rotation contributions to T1.

In an attempt to understand the temperature dependence ofT1 in these media and to further elaborate the dynamic behaviorof H2 in C60, we measured the values of T1 for the proton inHD in toluene-d8 and in HD@C60 dissolved in toluene-d8 forcomparison with the values for H2 under the same conditions.The use of HD as a relaxation probe allows for examining

changes in the following properties relative to H2: (1) themagnetic parameters7 responsible for T1 differ significantly fromthose for H2, (2) the difference in moments of inertia betweenthe two molecules leads to a different rotational energy spectrumand rotational state populations,8 and (3) the increase in massof HD and the shift of center of mass relative to the location ofthe proton via the motion of HD as a “loaded sphere”,9 changesto some extent the average position of the proton in HD relativeto H2 in the solvent or C60 cages and affects the interaction ofthe molecule with the surrounding medium.

As will be seen, (1) the difference in magnetic parametersmakes possible an additional test of the applicability of theanalysis of the dynamics of reorientation for HD using theHubbard theory for relaxation in liquids2 than was possible withH2 alone. (2) The rotational energy differences may be used toassess the applicability of a gas phase model, which requiresaveraging over rotational states.10,11 (3) The mass and center ofmass differences, on the other hand, give rise theoretically,9a tochanges in the average location of the protons in the twomolecules within the solvent cage9b or relative to the π-electronsof the C60 capsule, which could, in principle, manifest itself ina detectable difference in chemical shift between HD and H2 inthe two environments.

We have already made use of a fourth difference12 betweenHD and H2, the absence of ortho and para isomers in the former,by employing HD and HD@C60 as intensity standards for studiesof the p-H2-o-H2 conversion in H2 and H2@C60. Although theproton T1 of pure HD (or HD as an impurity in H2 or D2)gas,13a,14 liquid,13b,15 and solid13c,15,16 has been reported, we arenot aware of a previous determination of T1 for HD in organicmedia. The detection of both H2 and HD peaks in the samesample and the resolution of the HD coupling constant, JHD,also makes it possible to measure JHD and the 1H chemical shiftdifference between the two species in the two media over arange of temperatures as a probe of the changes of theseparameters compared to experimental17 and theoretical18 deter-minations for H2 and HD in the gas phase.

† Part of the “Michael R. Wasielewski Festschrift”.* To whom correspondence should be addressed. E-mail: njt3@

columbia.edu.‡ Columbia University.§ Kyoto University.| Brown University.⊥ Current address: Department of Chemistry and Bioengineering, Rice

University, Houston, Texas 77005.

J. Phys. Chem. B 2010, 114, 14689–14695 14689

10.1021/jp102860m 2010 American Chemical SocietyPublished on Web 06/24/2010

Experimental Section

Materials. Calcium hydride (CaH2) powder, reagent grade,was purchased from Sigma Aldrich with 90-95% purity.Deuterium oxide (D2O) D, 99.9% and toluene-d8 D, 99.5% wereobtained from Cambridge Isotope Laboratories, Inc. Mixturesof H2@C60 and HD@C60 were synthesized by Komatsu and co-workers.19 Argon gas was purchased from TechAir.

Sample Preparation. CaH2 was carefully loaded into around-bottom flask and the apparatus to generate H2+HD gaswas assembled and purged with argon for 5 min. Approximatelyfive drops of D2O was carefully added dropwise with a plasticsyringe into the round-bottom flask. Mixtures of the HD andH2 gas generated were bubbled directly into a Wilmad, “J.Young Valve” NMR tube containing 600 µL toluene-d8 thatwas purged with argon prior to the addition of the HD/H2

mixture.In a separate J. Young tube, 2 mg of H2@C60+HD@C60

mixture was dissolved in 600 µL toluene-d8. The resulting purplesolution was bubbled with argon for 5 min prior to measurements.

NMR Measurements. T1 measurements were taken between200 and 340 K with temperature increments of 20 K. Spectrawere obtained on a Bruker DMX-500 NMR spectrometer. Theoperating frequency for 1H was 500.13 MHz. For the spin-latticerelaxation time, T1, at each temperature, the sample was allowedto equilibrate for 15 min or until the shimming, as monitoredby the lock-signal, was stable prior to data acquisition. The 90°pulse was recalibrated at each temperature. T1 measurementswere performed using the inverse-recovery pulse sequence:relaxation delayf πf τf π/2f acquire, with 13 values forthe variable delay τ, in the ranges 0.001-2.5 s and 0.001-20s for H2/HD@C60 and H2/HD, respectively. A recycle delay

between pulses of 2.5 s was used for H2/HD@C60 and 25 s forH2/HD. T1 values were calculated for the H2 peak and each ofthe peaks of the HD triplet (Figure 1) assuming first-orderrecovery. The digital resolution was 0.18 Hz/point. The standarddeviations for fitting the H2 and the HD data were notsignificantly different, which we take to imply that anynonexponential contribution to HD relaxation is undetectablein our data, which is consistent with an insignificant contributionfrom 2H-1H cross-relaxation.9,10

Results & Discussion

A. Spin-Lattice Relaxation Times. Figure 1a shows atypical spectrum of the H2/HD mixture. Figure 1b shows thevalues of the relaxation rate, 1/T1, for H2 and HD in toluene-d8

and in C60 over the temperature range 200-340 K. The valuesfor H2 in the H2/HD mixture in both environments are indis-tinguishable from those reported previously.1 The values of T1

determined for each of the three lines of HD were the samewithin experimental error, and only the average value is shownin the figure. The value of the relaxation rate for HD isconsistently smaller than that for H2. As observed previously,H2 relaxation in both media as a function of temperature passesthrough a shallow minimum,1,5 whereas the relaxation rate forHD increases monotonically with temperature.

The above observations support the qualitative idea thatrelaxation of 1H in HD is dominated by the spin-rotationinteraction over the entire temperature range studied. This is incontrast to H2, where the dipole-dipole interaction between theprotons becomes of greater importance than the spin-rotationinteraction at low temperatures. The observations for HD areconsistent with the 6-fold decrease in the magnitude of the 2H

Figure 1. 1H NMR spectra (a) and relaxation rates (1/T1) (b) of toluene-d8 solution of a H2/HD mixture (top) and a toluene-d8 solution of H2/HD@C60 mixture (bottom). Estimated errors in relaxation rates are within the width of the symbols on the plots.

14690 J. Phys. Chem. B, Vol. 114, No. 45, 2010 Chen et al.

magnetogyric ratio, which greatly reduces the dipole-dipoleinteraction. As expected, the spin-rotation interaction becomesincreasingly effective at high temperature. The substantialenhancement of the relaxation rate of HD in the C60 cageparallels that observed for H2 and may be similarly attributedto the reduced mobility of the incarcerated hydrogen molecule.

B1. Theoretical Analysis of T1’s. The qualitative behaviorof the relative 1H relaxation times of H2 and HD is as expectedfor the change in the magnitude of the magnetic parameters inthe two isotopomers. But what of the quantitative picture? Formore than 50 years, the relaxation times of 1H and 2H in H2

and its isotopomers have been employed as a tool to extractinformation about the dynamics of molecular hydrogen in avariety of environments. The theoretical models have been ableto exploit knowledge of the magnitudes and anisotropies of theparameters describing the spin-rotation, nuclear spin dipole-dipole, and, in the case of 2H, nuclear quadrupole interaction,obtained from pioneering molecular beam resonance measure-ments carried out even before the modern era of NMR.7,20

As in our previous report,1 the starting place for a morequantitative interpretation of the T1’s will be the assumptionthat only intramolecular interactions contribute to T1, leavingthe interesting field of intermolecular relaxivity21 of HD relativeto H2 to other studies.22 It is also assumed that the modulationof these interactions is related primarily to the rotational degreesof freedom of the molecule through changes in orientation orrotational angular momentum. Within this approximation, thetheoretical challenge then becomes deciding how to describethe way the intramolecular interactions are affected by thedynamics of the hydrogen molecule. Two limiting models havebeen employed, which might be called, after Gordon,23 the “J-diffusion” and “m-diffusion” models, where J and m are thequantum numbers for the principal value of the rotational angularmomentum and its z-component, respectively. In the formermodel, it is assumed that collisions produce transitions amongall of the molecular rotational states on a time scale suitablefor inducing the nuclear spin state transitions required forspin-lattice relaxation. Such collisions also are implicit in theHubbard theory2 for relaxation in liquids. That model seems tobe especially appropriate for heavy molecules with closelyspaced rotational states or, possibly, small molecules in astrongly interacting medium. It gives rise to separate correlationtimes for rotational angular momentum and reorientation,although, as Hubbard has shown,2 for large molecules these maybe related. We employed this model to analyze our earlier workon H2 relaxation1 and for the sake of completeness will applyit to the current results.

At the other extreme is the m-diffusion model first proposedby Schwinger and Bloembergen3 to describe intramolecularrelaxation of H2 in the gas phase. It assumes that the total angularmomentum, J, is preserved for a time that is too long tocontribute to T1, relaxation occurring instead via more rapidreorientation of the vector J among the values of its mcomponents. Changes in J do occur sufficiently rapidly,however, to yield a single relaxation time that is averaged overthe thermally accessible values of J. While it might seemunlikely that a model developed to describe relaxation in thegas phase would be applicable to H2 in condensed media, weare encouraged to apply it to the current results by recentspectroscopic studies, which show that the translation-rotationstates of H2 in H2@C60

24 and an open fullerene cage25 are well-resolved. These results are similar to the observation some timeago that the rotational Raman spectrum of H2 in liquid water26a

and ice26b and neutron scattering of H2 in ice26c exhibit well-

resolved peaks with widths corresponding to rotational statelifetimes on the order of picoseconds. Studies of soundpropagation in hydrogen gas also attest to the relative inef-fectiveness of collisions in bringing about changes in J,27

although the number of collisions required is smaller for HDinteracting with the noble gases.28

B2. J-Diffusion/Hubbard Model. We have applied both ofthe above models to the analysis of the T1 measurements forH2 and HD. In applying the J-diffusion model, we have usedthe formulation of Hubbard to separately estimate the correlationtimes for the dipole-dipole interaction, τdip,HY, and spin-rotationinteraction, τsr,HY, (Y ) H or D) over the entire temperaturerange studied. The observed spin-lattice relaxation rate, 1/T1,HY,is related to these two correlation times by eq 1

As eq 1 shows, each contribution to the relaxation rate maybe expressed as the product of a factor involving the temper-ature-averaged square of the angular momentum, J, using themoment of inertia, IHY, the nuclear spin angular momentum,IY, an angular frequency factor, CHY or ωHY, and the appropriatecorrelation time, τsr,HY or τdip,HY. Equation 1 is derived on theassumption that the observation frequency, ω0 ) 3.1 × 109 rads-1 (at 500 MHz) is much smaller than 1/τ. Using the knownmolecular constants7 for H2 and HD, the coefficients multiplyingeach of the four varieties of τ can be readily calculated (rad2

s-2): CHH2 ) 0.51 × 1012; CHD

2 ) 0.29 × 1012; ωHH2 ) 5.20 ×

1012; ωHD2 ) 0.22 × 1012. When written this way, it becomes

clear that T1’s on the order of 1 s yield correlation times on theorder of 1 ps, assuring that ω0τ is much less than 1.

The challenge is how to employ eq 1 to use two observables,T1,HH and T1,HD, at each temperature, to calculate four correlationtimes. In order to accomplish this, we have assumed, somewhatin the spirit of the J-diffusion approximation, that the corre-sponding correlation times are the same for H2 and HD at agiven temperature. This would hold if the reorientation dependsprimarily on the potential energy of interaction betweenhydrogen and the medium, which should be nearly the samefor the two isotopomers, but is insensitive to the translationalor rotational kinetic energy of the molecule. The values of τsr

and τdip can be obtained in this way by straightforward algebraicmanipulation of eq 1 for H2 and HD at each temperature. Thevalues obtained are shown in Figure 2 for the toluene-d8 andC60 environments. The qualitative features of this analysis maybe summarized as follows: (1) Both correlation times are anorder of magnitude longer for HY in C60 than in toluene-d8,consistent with our earlier analysis.1 It is consistent with ourearlier proposed model in which the rotation of HY is slowedby some degree of interaction with the slowly rotating C60 cage.(2) The angular momentum correlation time, τsr, is generallylonger than that for reorientation, τdip, at all temperatures. Thisis qualitatively consistent with m-diffusion-type behavior.

B3. m-Diffusion/Johnson-Waugh-Bloom-Oppenheim. Inapplying the m-diffusion model, we have used the extensionby Johnson and Waugh10 of the original model to include HD.Their formulation also incorporates separate correlation times

T1,HY-1 )

2⟨J2⟩HYCHY2

3τsr,HY + ωHY

2τdip,HY

⟨J2⟩HY ) 2IHYkBT/p2ωHY2 )

4κHYγH2γY

2p2

3rHY6

IY(IY + 1)

κHH ) 3/2; κHD ) 1(1)

H2 and HD in Toluene-d8 and H2/HD@C60 J. Phys. Chem. B, Vol. 114, No. 45, 2010 14691

for the dipole-dipole and spin-rotation contributions to T1,which in principle depend on the rotational state, J. The observedT1 in this case represents a Boltzmann average over thermallyaccessible states with populations pJ.

We have estimated values of the thermally averageddipole-dipole correlation time, τsr, separately for H2 and HDby using the relation in eq 3 between τdip and τsr derived byBloom and Oppenheim11 for relaxation of H2 at low pressures.If it is further assumed that the J-dependence of either τdip orτsr is weak,

it possible to compare a single approximate correlation time,which we choose to be τsr, for HD and for H2 in bothenvironments. The values of τsr at each experimental temperatureare shown in Figure 3. There is a striking qualitative similaritybetween the values and temperature dependence of the correla-tion times shown in Figures 2 and 3. As with the Hubbardmodel, there is a distinctly longer correlation time for eitherisotopomer in C60 compared to toluene-d8. Also revealed,however, is the additional information that HD has a somewhatlonger τsr than H2 in the same environment, the difference beingsomewhat greater in C60 than toluene-d8. This is opposite tothe effect observed for noble gas collisions in the gas phase(Vide infra). The relatively small differences between the values

of τsr for HD and H2 is roughly consistent with the assumptionused in applying the J-diffusion model that the correspondingcorrelation times are the same for both species.

C. Comparison with Noble Gas Collision Data. There havebeen a number of studies of the effects of noble gas collisionson the relaxation times of nuclei in all three of the hydrogenisotopomers. The principal goal of these studies has been tocharacterize the anisotropic part of the intermolecular potential,which brings about changes in the rotation of the hydrogenmolecule.4 Of relevance to the present study are measurementsof the proton relaxation times of H2-He,14c HD-He,14a H2-Ar,14d and HD-Ar14b mixtures over a range of temperatures andgas densities. The most significant qualitative difference betweenthese results and those reported here is the much longer T1 ofHD compared to H2 at the same temperature and collision gasdensity. The qualitative explanation for at least a portion14a ofthis effect is the fact that HD can readily undergo ∆J ) ( 1rotational transitions, whereas ortho-H2 is restricted to ∆J )(2 transitions.9a An additional, perhaps more important effectis that the lower symmetry of HD compared to H2 allows it toprobe a wider range of anisotropy of the interaction potential.14a

This leads to significant shortening of the lifetimes of HD spinstates, corresponding to τsr and τdip in eqs 1 or 2, with consequentdecrease in the relaxation rate. The ratios of T1’s for HD andH2 in the gas phase are compared with those in toluene-d8 andC60 in Figure 4. The gas phase data shown in Figure 4 wereobtained in the high-density region where the spin state lifetimeis short compared to the larmor frequency. In this region, T1

increases linearly, that is, 1/T1 varies inversely, with densitybecause of the decreased lifetime of the spin states as theprobability of collision with a gas molecule increases. We havetherefore shown the ratio of the T1’s at the same density. It isclear that, at all temperatures in all media, T1,HD is longer thanT1,H2 and that the ratio increases as the temperature decreases,as is expected for a relative increase in the contribution ofdipolar relaxation in H2 at lower temperatures. It is also notablethat the ratio for HY@C60 (Y ) H or D) varies less than forthe other conditions, changing only 2-fold over the entiretemperature range studied. A qualitative explanation for thiswould be a shorter correlation time for H2 rotation in thecondensed media, which compensates somewhat for the weakermagnetic interactions in HD compared to H2.

One possible explanation for the striking difference inbehavior of the relative relaxation rates of HD and H2 in thegas and condensed phases is shown in Figure 5. We havecompared on a semilog scale the actual values of 1/T1 in thecondensed phase to those in the gas phase at a molecular density,209 amagat (amg), corresponding to liquid toluene at 300 K.The most striking results are (1) the similarity of the relaxationrates of HD in C60 to those induced by collisions with He orAr, (2) the substantially slower relaxation of both HD and H2

Figure 2. Correlation times for spin-rotation interaction, τsr, (triangles)and dipole-dipole interaction, τdip, (circles) for HY in toluene (opensymbols) and HY@C60 (filled symbols) from the Hubbard model. Seetext for details.

Figure 3. Spin-rotation correlation time, τsr, for HY in toluene (opencircles) or in C60 (filled circles) for H2 (red) and HD (blue) from them-diffusion model. See text for details.

T1,HY-1 ) ∑

J

pJT1J,HY-1

T1J,HY-1 )

2J(J + 1)CHY2

3τsrJ,HY + J(J + 1)

[(2J - 1)(2J + 3)]ωHY

2τdipJ,HY

(2)

τdipJ

τsrJ) (2J - 1)(2J + 3)

3(4J2 + 4J - 7)(3)

Figure 4. Comparison of T1HD/T1H2 in toluene-d8, C60, and in Ar andHe buffer gas. See text for details.

14692 J. Phys. Chem. B, Vol. 114, No. 45, 2010 Chen et al.

in toluene-d8 compared to the gas phase, and (3) the substantiallyslower relaxation of H2 in C60 compared to the gas phase. Result1 could be explained by invoking ∆J ) (1 transitions for HDwith similar rates in C60 and in collisions with He or Ar atoms,and result 2 is consistent with more rapid reorientation of bothHD and H2 in toluene-d8 compared to collisions with He or Ar.Result 3, however, requires the surprising conclusion that therotational states of H2 in C60 have a significantly shorter lifetimethan in collisions with the noble gases at similar densities. Thissuggests a significant enhancement of the rate of ∆J ) (2transitions or of transitions among the m-states of a given J-state.Wesuggest that this resultmayberelatedto therotation-translationcoupling predicted29 and observed spectroscopically24,25 andthermochemically30 for H2@C60 and other endo-H2 fullerenes.

D. Other Measurements. In addition to determining therelaxation times in HD and H2, we have measured three ad-ditional NMR parameters over the range of temperatures studied:(1) the chemical shift difference between HD and H2 in solutionand in C60, (2) the magnitude of JHD, and (3) the widths of theH2 and HD peaks. As discussed below, in all cases we havedetected only small, but possibly significant, effects of encap-sulation on these parameters.

D1. Chemical Shift Comparison. The 1H chemical shift ofHD relative to H2 was measured as a function of temperatureover the range 200-340 K in toluene-d8 and in C60 (See FigureSI1, Supporting Information). In both environments, the chemi-cal shift difference decreased monotonically with increasingtemperature, by about 2.5 parts per billion (ppb) in toluene-d8

and 3 ppb in C60. At each temperature, the chemical shiftdifference was 1-2 ppb smaller in C60 compared to toluene-d8.The difference is also several percent smaller than observed andcalculated for H2/HD in the gas phase18,31 and has a similartemperature dependence. Such effects have been termed a “siteeffect” as applied to the density dependence of the NMR isotopeshift in hydrogen18c and may be related to the shift in the centerof mass in HD.9

D2. 1H-2H Spin-Spin Coupling. The value of the spin-spincoupling parameter, JHD, measured as one-half the frequencyseparation of the outer lines of the HD triplet, was alsodetermined in the two environments (see Figure SI2, SupportingInformation) over a range of temperatures. It was found thatJHD is independent of temperature, but is consistently smallerby about 2% in C60 than in toluene-d8. Furthermore, JHD in bothmedia is smaller by ca. 1-2% than observed in the gas phase.17a

It is interesting to note that the smaller value of JHD in thecondensed media is consistent with the report that JHD decreaseson going from the gas to liquid phases18b and is supported bycalculations predicting a decrease in JHD with small decreasesbond length, although dramatic reductions in JHD have also beenobserved in Os-HD complexes where the HD bond order ismarkedly decreased.32

D3. Linewidth Comparison. The spectra shown in Figure 1display noticeably narrower lines for HD than for H2. It hasalso been noted previously33 that the 1H NMR lines of HD inan open fullerene cage are noticeably narrower than those ofH2, suggesting to the authors that the difference in relaxationtimes may be due to the larger dipole-dipole interaction in thelatter. This is fully consistent with the observation reported herethat the T1 of HD is longer than the T1 for H2 at all temperatures.In the case of HD, however, there is the potential for anadditional contribution to the line width from “scalar relaxationof the second-kind” via quadrupole relaxation of the 2H (I ) 1)nucleus.34 This line width contribution, which produces effectssimilar to chemical exchange, has been detected previously ingas-phase HD as a slight decrease in the value of JHD arisingfrom incipient collapse of the spin-spin triplet.35 A moredetailed analysis of the phenomenon, also predicts selectivebroadening of the outer lines of the multiplet. The latter effectis well-documented34 for the related example of the contributionof 14N quadrupole relaxation to the appearance of the multipletin 14NH3.

In an initial effort to assess whether the above effects can beobserved in our samples, we have estimated the magnitude ofany broadening of the HD peaks beyond the contributions fromprocesses reflected in T1 and magnetic field inhomogeneity. Theformer contribution to the line width was assumed to be thesame as 1/T1. The latter was estimated from the observed linewidth for H2 by subtracting the calculated T1 contribution,assuming that any additional broadening arises from fieldinhomogeneity and is the same for H2 and HD. Figure SI3 (seeSupporting Information) shows the values of the residual linewidth for each of the three peaks for HD in solution and in C60

over a range of temperatures. As can be seen from the figure,there seems to be a trend toward a residual line width of ca.0.5 Hz for HD in C60 but not in toluene-d8. If the excessbroadening arises from relaxation of 2H, this would correspondto a 2H T1 on the order of 3 s. This is, in fact, strikingly similarto the value of T1 for 2H measured in preliminary experimentson D2@C60.36 We were, however, unable to detect a statisticallysignificant difference between the intensities of the middle andouter lines of the HD triplet, which would have indicatedselective broadening due to quadrupole relaxation of the 2Hnucleus. Furthermore, the expected decrease in measured JHD

due to incipient collapse of the multiplet would be expected tobe greatest at low temperatures, where slowed rotation of theHD molecule should give rise to faster relaxation of the 2Hnucleus by the quadrupole mechanism. As described above,however, it is observed that JHD is independent of T over therange studied.

Summary and Conclusions

The values of T1 have been measured from 200-340 K forthe protons in H2 and HD molecules dissolved in toluene-d8

and incarcerated in C60 dissolved in toluene-d8. The qualitativeobservations are that HD relaxes more slowly than H2 in allmedia and at all temperatures. This is to be expected based onthe somewhat smaller value of the spin-rotation interaction andthe much smaller dipole-dipole coupling in HD compared toH2. In an effort to develop a more detailed picture of thedynamics of molecular hydrogen in solution and C60, the datawere analyzed in three ways:

(A) Correlation times for angular momentum and orientationwere estimated using a model developed by Hubbard2 andGordon23 and others that invokes a classical average of therotational angular momentum, J, to treat the spin-rotation

Figure 5. Relaxation rates, 1/T1, (log scale) for H2 (red) and HD (blue)in toluene (open circles), C60 (filled circles), Ar at 209 amg (opensquares), and He at 209 amg (open triangles). See text for details.

H2 and HD in Toluene-d8 and H2/HD@C60 J. Phys. Chem. B, Vol. 114, No. 45, 2010 14693

contribution to T1, and diffusional reorientation to describe thedipole-dipole contribution. By assuming that the correlationtimes for angular momentum, τsr, and orientation, τdip, are similarfor H2 and HD, it is possible to extract the values of theseparameters from the T1 data in toluene-d8 and C60 at eachtemperature. The results confirm our previous conclusions1 forH2 alone, based on the assumption that the spin-rotationmechanism dominates at high temperature and the dipole-dipolemechanism at low temperature. In brief, Figure 2, shows bothcorrelation times are substantially shorter for HY in toluene-d8

than in C60 and that τsr is somewhat longer than τdip at alltemperatures.

(B) An m-diffusion model in which the magnitude of Jchanges less rapidly than its m orientational components, hasbeen used to relate the observed T1 to a thermal average ofJ-dependent T1’s. It is also assumed that a J-dependent relationexists between the correlation times for the spin-rotationinteraction, τsr, and the dipole-dipole correlation time, τdip, asproposed by Bloom and Oppenheim.11 It is further assumed thatτsr depends only weakly on the value of J. Under thisassumption, the population weighted average T1 then dependson a single correlation time, chosen to be τsr, at each temperature.As shown in Figure 3, in both media the correlation time forH2 is shorter than for HD, implying faster redistribution amongthe rotational substates in the former than the latter. Thedifference is greater for HY@C60 than in solution.

(C) The ratios of T1’s for HD and H2 in condensed mediaare compared with those resulting from collisions with He orAr atoms in the gas phase (Figure 4). The measured values incondensed media are also compared with those estimated forgas phase collisions at the same molecular density as liquidtoluene (Figure 5). It is found that the relaxation rates for bothHD and H2 in toluene-d8 are much slower than in the gas phase,which would be consistent with shorter collision times in toluenecompared to He or Ar at the same density. Surprisingly,however, the relaxation times of H2 and HD in C60 are similarto that estimated for HD in a He or Ar. This suggests that therelaxation time of H2 in C60 is shortened relative to what it wouldbe if only ∆J ) (2 rotational transitions were allowed, as inthe gas phase.

The qualitative picture that emerges from the aboveanalyses is that transitions among the rotational states ofH2 occur at a rate similar to those of HD in both toluene-d8

solution and in C60. This is in sharp contrast to the situationfor transitions occurring as a result of collisions with He orAr in the gas phase, where the lifetimes of the rotationalstates of HD are considerably shorter than those for H2. Thegas phase result is consistent with the expectation that HDcan readily undergo ∆J ) (1 transitions, whereas ortho-H2

transitions are restricted to ∆J ) (2. We suggest that thiscontrast may be related to the rotation-translation couplingof H2 incarcerated in C60, an explanation that is beginningto be revealed by both theoretical and experimental studies.The results for HY in toluene-d8 also suggest a similar, thoughpossibly less easily defined, shortening of the rotational statelifetimes of H2 in solution.

Measurements of the relative 1H chemical shifts of H2 andHD, the value of JHD, and the widths of the HD peaks at varioustemperatures revealed only small effects with insufficient ac-curacy to warrant more detailed interpretation in this report.Measurements with higher spectrometer resolution, directmeasurement of transverse relaxation times, T2, and determi-nation of T1’s and other parameters for 2H in HD and D2 in theenvironments studied here, using instrumentation not readily

available in the present study, would, however, clearly be ofvalue in rounding out the description of the dynamics of H2 insolution and in the fullerenes and should provide a better testof the theoretical models used in the present work. It wouldalso be of interest to extend solid-state NMR relaxation studiesof H2@fullerenes37 to the corresponding HD compounds. Ofparticular interest should be the ability to probe more effectivelyat very low temperatures the role of the J ) 0 ground rotationalstate, which, in principle, cannot contribute to either thespin-rotation or dipole-dipole interaction.13a

Acknowledgment. The authors at Columbia thank the NSFfor its generous support of this research through Grant CHE 0717518.

Supporting Information Available: Graphs resulting frommeasurements of (1) the chemical shift difference between HDand H2 in solution and inside C60, (2) the magnitude of JHD

spin-spin coupling, and (3) linewidths of the H2 and HD peaks.This material is available free of charge via the Internet at http://pubs.acs.org.

References and Notes

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